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Slope Stability Analysis Using Genetic Algorithm

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Slope Stability Analysis Using Genetic Algorithm SLOPE STABILITY ANALYSIS USING GENETIC ALGORITHM A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Bachelor of Technology in Civil Engineering By ANURAG MOHANTY 10501005 Department of Civil Engineering National Institute of Technology Rourkela-769008 2009 National Institute of Technology Rourkela CERTIFICATE This is to certify that the thesis entitled “SLOPE STABILTY ANALYSIS USING GENETIC ALGORITHM” submitted by Sri Anurag Mohanty, Roll No. 10501005 in partial fulfillment of the requirements for the award of Bachelor of Technology degree in Civil Engineering at the National Institute of Technology, Rourkela is an authentic work carried out by him under my supervision and guidance. To the best of my knowledge, the matter embodied in the thesis has not been submitted to any other University/Institute for the award of any Degree or Diploma. Date: (Prof. S.K. DAS) Dept. of Civil Engineering National Institute of Technology Rourkela-769008 ACKNOWLEDGEMENT I wish to express my deep sense of gratitude and indebtedness to Dr. S.K. DAS, Department of Civil Engineering, N.I.T., Rourkela for introducing the present topic and for his inspiring guidance, constructive criticism and valuable suggestions throughout the project work. .I am also thankful to all staff members of Department of Civil Engineering, NIT Rourkela. Lastly, I would like to thank and express my gratitude towards my friends who at various stages had lent a helping hand. Date: ( Anurag Mohanty) Abstract Analysis of stability of slopes is of utmost importance as its failure may lead to loss of lives and great economic losses. Failure of a mass located below the slope is called a slide. It involves downward and outward movement of entire mass of soil that participates in failure. Slides may occur in almost nay conceivable manner slowly or suddenly, with or without apparent provocation. In the present day lots of methods are available to the modern engineer to obtain the stability of slopes. Some are quite rigorous, while some are expensive. In this project a comparative of study of such methods has been done with special stress on the application of GA in the analysis of slope stability. 4 CONTENTS Chapter 1……………………………………………………….6 Introduction…………………………………………………………………..7 Slope Stability………………………………………………………………...7 Types of slope failures………………………………………………………..7 Use of Slopes…………………………………………………………………10 Chapter 2……………………………………………………….11 Methods of analysis…………………………………………………………..12 Tools and Packages available…………………………………………………15 Tool Adopted…………………………………………………………………17 Theory of slices……………………………………………………………….19 Method of Iteration………………………………………………………......22 Method Adopted (Bishop’s Method)………………………………………...24 Analysis by Slope…………………………………………………………….26 Results of analysis……………………………………………………………30 Chapter 3……………………………………………………….31 Genetic Algorithm…………………………………………………………....36 Methodology…………………………………………………………………36 Development of objective function…………………………………………..32 Flowchart of Bishop’s Method………………………………………………44 Output obtained from coding of Bishop’s method…………………………..45 Conclusion…………………………………………………………………....46 References……………………………………………………………………47 5 CHAPTER 1 WHAT IS SLOPE? 6 INTRODUCTION A slope may be an unsupported or supported, inclined surface of some mass like soil mass. Slopes can be natural or man made. These may be above ground level as embankments or below ground level as cuttings. SLOPE STABILITY In naturally occurring slopes like along hill slopes and river sides, the forces of gravity tends to move soil from high levels to low levels and the forces that resist this action are on account of the shear strength of the soil. Presence of water increases weight and reduces shear strength and hence decreases stability. Weights of man made structures constructed on or near slopes tend to increase the destabilizing forces and slope instability. Causes of failure of Slopes: The important factors that cause instability in slope and lead to failure are 1. Gravitational force. 2. Force due to seepage of water. 3. Erosion of the surface of slope due to flowing water. 4. The sudden lowering of water adjacent to the slope. 5. Forces due to earthquakes. 7 TYPES OF SLOPE FAILURES 1. Rotational Failure This type failure occurs by rotation along a slip surface by downward and outward movement of the soil mass. Slope circle failure: In this case the failure circle intercepts the surface of the slope itself above the toe. Toe circle failure: In this case the failure circle passes through the toe of the slope. This occurs in steep slopes of homogenous soils. Base circle failure: In this case the failure circle passes below the toe at a depth ndH from top of the slope of height H. Such cases occur when slopes are flat with weak soil and a steep stratum occurs below the toe. Translational Failure Translational failure occurs in an infinite slope along a long failure surface parallel to the slope. The shape of the failure surface is influenced by the presence of any hard stratum at a shallow depth below the slope surface. These failures may also occur along slopes of layered materials. Compound Failure A compound failure is a combination of the rotational slips and the translational slips. A compound failure surface is curved at the two ends plane in the middle portion. A compound failure generally occurs when a hard stratum exists at considerable depth below the toe. Wedge Failure A failure along an inclined plane is known as plane failure or wedge failure or block failure. This failure may occur both in infinite and finite slope consisting of two different materials or in a homogeneous slope having cracks, fissures, joints or any other specific plane of weakness. Miscellaneous Failure 8 In addition to above four types of failures, some complex type of failures in the form of spreads and flows may also occur. Various types of failures are shown in FIG 1.1, 1.2 and 1.3. Failure of a road embankment Failure of a hill slope 9 Landslide In determining the stability of slope, first a potential failure surface is assumed and the shearing resistance mobilized along the surface is determined. This is the force that resists the movement of soil along the assumed failure surface and is known as resisting force. The forces acting on the segment of the soil bounded by the failure surface and the ground level are also determined and these forces attempt to move the soil segment along the failure surface. This is known as the activating force .The factor of safety of the segment is as follows Factor of safety for rotation = Moment of the resisting force Moment of the activating force Factor of safety for translation = Resisting force Activating force SLOPES ARE USED FOR:- Railway formations Highway embankments Earth dams Canal banks River training works Levees 10 CHAPTER 2 ANALYSIS OF SLOPE 11 METHODS OF ANALYSIS The analysis of stability of soil consists of two parts: The determination of the most severely stressed internal surface and the magnitude of the shearing stress to which it is subjected. The determination of the shearing strength along this surface. General Consideration and Assumptions in the Analysis The general assumptions in the analysis are: 1. The stress system is assumed to be two-dimensional. The stresses in direction which is perpendicular to the section of soil mass are taken as zero. 2. It is assumed that the coulomb equation for shear strength is applicable and the strength parameters c and ø are known. 3. It is assumed that the seepage conditions and water levels are known, and the corresponding pore water pressure can be estimated. 4. The conditions of plastic failure are assumed to be satisfied along the critical surface. In other words, the shearing strains at all points of the critical surface are large enough to mobilize all the available strength. 5. Depending upon the method of analysis, some additional are assumptions are made regarding the magnitude and distribution of forces along various planes. METHODS OF ANALYSIS OF STABILITY OF SLOPE The following methods are used for the analysis of stability of slopes. 12 1. Fellenius method 2. Swedish slip circle method 3. Bishop’s method 4. Janbu’s method 5. Friction circle method 6. Taylor’s stability number method 7. Culmann’s method 8. Spencer’s method 9. Morgenstern and price method 10. Bell’s method Fellenius Method (The Ordinary Method of Slices) The Ordinary Method of Slices (OMS) was developed by Fellenius (1936) and is sometimes referred to as “Fellenius Method.” This method is applicable to soil slopes with both friction and cohesion. In this method, the forces on the sides of the slice are neglected. The normal force on the base of the slice is calculated by summing forces in a direction perpendicular to the bottom of the slice. Once the normal force is calculated, moments are summed about the center of the circle to compute the factor of safety. Factor of safety = ∑ [с′ ∆ℓ + (W cosα - u∆ℓ cos2 α) tanǿ] ∑W sin α Where c' and ǿ = shear strength parameters for the center of the base of the slice W = weight of the slice α = inclination of the bottom of the slice u = pore water pressure at the center of the base of the slice 13 ∆ℓ = length of the bottom of the slice Swedish Slip Circle Method This method is also known as method of slices. This method was proposed by Petterson . It assumes a circular surface of failure and that the resistance is the total cohesion developed along the circle of failure. This method is applicable to purely cohesive soil and soil possessing both cohesion and friction. Purely cohesive soil (Øu = 0) Factor of safety = (cu L ar) / Wx Soil possessing both cohesion and friction ( c – Ø analysis ) Factor of safety = (c ∑ ∆L + tan Ø ∑ N) / ∑Τ Where cu = unit cohesion L a = Length of the slip arc r = Radius of the slip circle W = Weight of the soil of the wedge x = Distance of line of action of W from vertical line passing through the centre of rotation ∑Τ = algebraic sum of all tangential components ∑N = sum of all normal component ∑∆L = length of slip circle Bishop’s Method Bishop (1955) took into consideration the forces acting on the sides of the slices, which were neglected in the Swedish method.
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